Mathematics for the Million - Lancelot Hogben ***

This is one of the strangest maths books you are ever likely to encounter. Written in the 1930s and reissued in 2017, it's an attempt to provide mathematical instruction up to around A-level standard (though obviously the curriculum has changed a lot) for someone who, perhaps, doesn't respond well to the classroom and works better from self-teaching.

It's telling of the way popular science was considered in the period that apparently the author delayed publication as he was up for election to Fellowship of the Royal Society, which back then was dead against science popularisation.

Hogben, in a distinctive, mellifluous (if sometimes prolix) style, starts with the basics of arithmetic and leads us all the way through to calculus. Unlike his contemporaries, who were all for working through hundreds of geometry proofs for completeness, Hogben fills in the parts at each stage of mathematical development needed to reach the next stage and gives us no more.

The narrative here is very much centred on the application of mathematics through history. We see how geometry might have been used by Egyptian architects, and how trigonometry benefits those who need to navigate by the stars. The only problem with this learning-through-history approach is it can sometimes be hard to then relate what has been learned to uses in the present day.

Lancelot Hogben never intended this to be a fun read to pootle through just for the sake of it. The book is peppered with many exercises. It seems to be devised as a self-teach textbook of the future (as seen from the 1930s), throwing away the strictures of the rigid teaching approach of that period for something that is more approachable.

It's hard to say how well it delivers from the modern viewpoint of someone who has gone through all this stuff at school in a fairly traditional way. Clearly a lot of people decided it was a good approach back then: the book might not have made the 'million' in the title but certainly sold many copies.

To the modern eye, there is a danger of the book falling between two stools. It's not approachable enough to read purely for fun, but Hogben's distinctive, quirky style, combined with what is sometimes a rather tedious approach to the maths, means that it's not the best way for a modern reader, with no mathematical training, to learn about the subject. It stands best as a unique and fascinating oddity in the history of mathematical books for the general public - and as such is worth taking a look at.

Paperback:

Using these links earns us commission at no cost to you

Review by Brian Clegg

Comments

The Laws of Thought - Tom Griffiths *****

In giving us a history of attempts to explain our thinking abilities, Tom Griffiths demonstrates an excellent ability to pitch information just right for the informed general reader. We begin with Aristotelian logic and the way Boole and others transformed it into a kind of arithmetic before a first introduction of computing and theories of language. Griffiths covers a surprising amount of ground - we don't just get, for instance, the obvious figures of Turing, von Neumann and Shannon, but the interaction between the computing pioneers and those concerned with trying to understand the way we think - for example in the work of Jerome Bruner, of whom I confess I'd never heard. This would prove to be the case with a whole host of people who have made interesting contributions to the understanding of human thought processes. Sometimes their theories were contradictory - this isn't an easy field to successfully observe - but always they were interesting. But for me, at least, ...

The Infinity Machine - Sebastian Mallaby ****

It's very quickly clear that Sebastian Mallaby is a huge Demis Hassabis fan - writing about the only child prodigy and teen genius ever who was also a nice, rounded personality. After a few chapters, though, things settle down (I'm reminded of Douglas Adams' description of the Hitchhiker's Guide to the Galaxy ) and we get a good, solid trip through the journey that gave us DeepMind, their AlphaGo and AlphaFold programs, the sudden explosion of competition on the AI front and thoughts on artificial general intelligence. Although Mallaby does occasionally still go into fan mode - reading this you would think that AlphaFold had successfully perfectly predicted the structure of every protein, where it is usually not sufficiently accurate for its results to have direct practical application - we get a real feel for the way this relatively unusual company was swiftly and successfully developed away from Silicon Valley. It's readable and gives an important understanding of...

Nanotechnology - Rahul Rao ****

There was a time when nanotechnology was both going to transform the world and wipe us out - a similar position to our view of AI today. On the positive transformation side there was K. Eric Drexler's visions in the 1986 Engines of Creation. Arguably as much science fiction as engineering possibilities, it predicted the ability to use vast armies of assemblers to put objects together from individual atoms. On the negative side was the vision of grey goo, out of control nanotechnology consuming all in its path as it made more and more copies of itself. In 2003, for instance, the then Prince Charles made the headlines when newspapers reported ‘The prince has raised the spectre of the “grey goo” catastrophe in which sub-microscopic machines designed to share intelligence and replicate themselves take over and devour the planet.’ These days the expectations have been eased down a notch or two. Where nanotechnology has succeeded, it has been with the likes of atom-thick mat...

Search This Blog